Create A Simple Design
Create a PNG with your design using Windows Paint, Sketch, or Figma. The suggested resolution is 512x512 with a transparent background.
Generate the ICO Image With Retro Encabulator
Use an updated version of handy Linux edition of Rockwell Retro Encabulator, a.k.a. ImageMagick's convert utility to convert PNG into ICO file:
convert \
favicon.png \
-define icon:auto-resize=256,128,64,48,32,24,16 \
favicon.ico
Profit
Profit.